September, 1928
I N D U S T R I A L A S D ESGIA\-EERISG CHEXIXTRY
interest, depreciation, and maintenance costs, based on cost of plant of $100,000 interest a t 6 per cent, depreciation at 3 per cent and maintenarice 1 per cent. The maintenance costs to date have been practically nothing and in time will occur.
953
ACKXOWLEDGMEXT-The operation of the softening plant is in charge of H. C. Kneeland. F. B. Beech. the manager of the company, was largely responsible for the installation of the zeolite plant and furnished the cost figures and operating data.
Evaluation of Variable-Temperature Cures’ J. R. Sheppard and W. B. Wiegand T H E EICLE-PICHER LEADCO\IPAAY,JOPLIN,
Mo ,
\AD
BIAAEYA N D S M I T H C o , NEW Y O R K . N. V.
Employing the generally accepted empirical rule that schedules in terms of some N VULCAXIZIXG pracintensity of curing action doubles with a rise of 15” F., unit of curing effect-and tice “stepped cures,” or relations are developed between the several variables no longer is a ready soluschedules which comprise of a cure segment with a constant temperature gration available. Consea number of periods each subdient-viz., “intensity of curing action,” “curing quently, schedules involving Sect to either a constant temeffect,” time, and temperature-and the constants of variable temperature are perature or a uniform temsuch a cure, initial temperature and temperature generally handled on a perature gradient, are in gradient. purely empirical basis. general use. Cures of this Exact evaluation of cures is extended to schedules The curing effect of a qort are especially characterinvolving variable temperatures by the equations showperiod with a constant temistic of the footwear and ing curing effect as a function of the other properties perature may be evaluated proofed-goods branches of of a cure. These are the equations of chief practical as the product of time and the industry and are used importance. intensity of curing action. in the vulcanization of thick Curing effect, the measure of the net value of a schedobjects such as solid tires and Note-The expression “rate of ule in effecting vulcanization, may be determined for rubber rolls. For instance, a cure” has frequently been used t o a given schedule either by calculation from one of the “dry heat” or “box cure” for designate what herein is termed “effect” equations, by direct reading from one of the “intensity of curing action” befootwear, lasting in all from cause of the common, perhaps more several herein displayed graphs of effect us. other prop2 to 9 hours, may consist of proper, use of the former term t o erties, or by estimation of the area under an intensitythree to six well-defined designate a different quantity than time curve. periods. I n a typical case t h a t which we call “intensity”Intensity of curing action measures the importance of viz., t o designate the rate of change a box cure may have the in the properties of a given stock a t a temperature in promoting vulcanization, and the following parts: a preliminary a given instant. “Intensity” is a intensity-time curve displays the curing ability of a rise of one or two gradients; function of temperature only, someschedule in its various parts even more accurately than a “hold” a t a constant temthing independent of composition the more usual temperature-time curve. of stock or of time, and the writers perature adequate to dry out have therefore distinguished beExamples applying the methods of the paper to typifabric and rubber; a rise of tween intensity, I, and rate, R. cal factory cures are given. one or two gradients from The distinction between these the drying temperature to two quantities and their relation the highest temperature of the schedule, during which the in- to composition, C, time, 1, and temperature, T , are: I = h(T) tensity of the curing action is increasing; and finally a “hold” R = fzU, C, t ) = fi[fi(T), C. 11 a t a constant (comparatively high) temperature of such “ R a t e of cure,” as defined by this equation, approaches zero as a limiting duration as to bring the goods to the proper state of cure. value for any composition and temperature as the time is increased. This Where the heater is of large volume with air the medium, paper is not particularly concerned with rate: its purpose is the analysis of it is impossible, even if it were desirable, suddenly to impose vulcanizing schedules per se, independently of composition of stock or other which determine “rate of cure.” upon the stock the maximum curing temperature. Schedules variables Similarly “curing effect,” E , has been employed t o designate t h a t ith gradients, while from the practical standpoint both quantity depending only on intensity and on time according t o the equaunavoidable and desirable, present theoretical difficulties tion E = fI.dt =Jfi(T).dt arising from the lack of a measure of their net curing effects. “effect” has been distinguished from “degree,” D , or state of cure as For example, it is evident that to double the effect of a given and defined by the equation constant-temperature cure it is necessary only to double the D = J R dl = Jfz(1, C, t).dt = J f z [ f i ( T ) , C, 11 dt time, to raise the temperature appropriately, or to increase Curing effect pertains t o a schedule, degree, or state t o a stock; we are conboth the time and the temperature according to easily com- cerned here only with t h e schedule. putable degrees. The inconvenience of a variable tegperAs schedules are defined originally in terms of temperatures ature within the period is not involved. However, let it be required to alter by a given amount the curing effect of a rather than intensities, a relation between these two quantypical footwear box heat; to reduce the total time of one, tities is necessary. Various relations have been used, the retaining, by internal changes in the schedule, the original most generally accepted being those which claim a doubling net effect; to assign relative curing values to several schedules of the intensity for a given temperature increment. For differing as to total time, maximum temperature reached, example. increments ranging from 11” to 18” F. have been period a t maximum temperature. and period and gradient of claimed as responsible for a doubling of the intensity. With, approach to maximum temperature; or to do anything else therefore, the proportionality of effect to time and to independent on the evaluation of several entirely different tensity and with the dependence of intensity upon temperature according to an empirical exponential relation, it is a 1 Presented under the title “The Evaluation of Variable Temperature very simple matter to evaluate a giyen constant-temperature Cures, with Special Reference t o Rubber Footwear and Proofed Goods period, or a more elaborate schedule consisting of a succession Schedules” before the Dirision of Rubber Chemistry a t the 75th Meeting of of such periods. the American Chemical Society, S t Louis, SI0 , April 16 to 19, 1928.
I
I 3 D CSTRIAL A X D EXGINEERIMG CHEiMlSTRY
954
It is not the purpose of this paper to discuss the validity of any one temperature-intensity relation as against another, but rather to show, on the basis of one such relation, generally accepted and quite well established, how exact evaluation may be extended quickly and conveniently to schedules with
VOl. 20, x o . 9
temperature and 240" F. has been arbitrarily chosen as the temperature of unit intensity. Let I equal the intensity of curing action, measured in such units that I = 1 n-hen T = 240. Then from the rule that intensity doubles nith a rise of 15" F., we have or
49 8 log I = T-240 To - 240 + ml whence from (1) I = 2 1.5
(3)
Simplifying the form by substituting the constants E
e=2
0 1.5
m -
b = 215 I = abt
and we have
(4)
I t should be observed that (2) and.(%) give intensity in terms of temperature, while (3) gives intensity in terms of time elapsed since the beginning of the period. TIME-CURIXG EFFECT RELaTIoK-Let E = curing effect, defined by the equation, holding for a constant value of I , E
=
It
T = 240) Under a temperature gradient, i. e., when I varies with t
so that E
=
1, when t
=
1, and I = 1 (or when
(5)
d E = I.dt
E =X I . &
and
variable temperatures. Several years ago, the authors, chiefly with the object of facilitating the consideration of vulcanizing schedules for footwear and proofed goods, developed the equations and convenient graphic methods which will be described herein. The relationships developed are general and apply to any schedule consisting of one or more parts, each characterized by a uniform temperature gradient. Development of Formulas
The writers have adopted the perhaps most commonly accepted relation between intensity of curing action and temperature-via., that intensity doubles with a rise of 15" F. Although one of them2 has found that, in mold cures on a litharge stock, 13" F. produces a doubling of the intensity, in this paper 15" has been used, because (a) the experimental work in question was confined to press cures and to a single stock, whereas the formulas herein developed and depending on an intensity-temperature relation had their application largely in dry heats, and also on account of ( b ) the general acceptance of and (c) ease of handling the 15" F. rule, Tables based upon this figure have been regularly employed by the industry to facilitate calculations on constanttemperature cures. I n analyzing the effect of a "stepped cure" it must first be divided into parts, each having a uniform rise (or fall) of temperature. TINE-TEMPERATURE R E L ~ T I O N - Lus ~ ~consider a period in which there is a constant temperature gradient-i. e , one in which =
E = Libt.dt
From (4)
E = - a- ( b t - l ) - a ( b t - I ) In b 0.04621 m
or
(6) CURIKGEFFECTINTENSITY AYD CURIKGEFFECT-TEMPERATURE RELATIom-From (4) and (6) we get I-a
E =
0.04621 m or I = 0.04621 mE From (2) and (8) we get
,v,4,"E'S RELATED
J,T
I
EQUATION USISG PRIMARY CONSTANTS
T-240
To-240 f mt 15
I = abt
E
+
Sheppard, "An Experimental Determination of t h e Temperature Coefficient of Vulcanization with Litharge" presented before the Division of Rubber Chemistry a t the 75th Meeting of the American Chemical Society, St. Louis, Mo., April 16 t o 19, 1928.
ECWATIONUSING SECONDARY CONSTANTS
I = Z T
Then the relationship between time and temperature is T = TO mt (1)
2
(8)
T-240
+
m, a constant
To = temperature a t the beginning of the period TEMPERATURE-INTENSITY AND TIME-INTENSITY RELATIONS -It is convenient to set the intensity a t unity for some given
a
(9) 0.04621 mE a = 2 l5 SUMMARY OF RELATIONS-By means of these equations, when for any curing period with a constant rate of temperature change there are given the constants To (initial temperature) and m( = d T / d t ) and any one of the four variables t, T, I , and E , the other three variables may be calculated. For convenience, the equations developed, together with obvious expansions of equations (6), (8), and (9), are summarized as follows:
dt where t = time in minutes since the beginning of the period and T = temperature in ' F. a t time t where
(7)
+
-
a(bt-1) 0.04621 m
To -240
I = 0.04621 mE
I,E
+2
I = 0.04621 m E
-To-240 _ _ E,T
I
I
0.04621mE+2.
302.5
_ =2
l5
To -
T
m E -k 215
= 215
T-24( 15
+a *T
0.04621 m E
f II = 2
15
September, 1928
ILYDI;STRIALAiYD ELYGINEERIXG CHEAVISTRY
Application to Cure Schedule Evaluation
INTENSITY OF CURIXG AcTIox-Intensity of curing action a t any given temperature may be obtained from equation (2) or @a); or, as a function of time, from ( 3 ) . These two relations yield straight lines when graphed on semilogarithmic paper. Figure 1, in which equation (2) has been so plotted, enables intensity to be read instantly for any given temperature with an accuracy of about 1 per cent, an accuracy exceeding the nicety with which equation (2) conforms to the facts. Intensity is a quantity of importance per se in that it is the function which must be known whenever it is desired to transform, without change in curing effect, a constant-temperature cure from a given to a new time and temperature. Such transformations are made according to equation (5), and in general any problems on constant-temperature cures involving the three variables of time, temperature, and curing effect are handled by equation ( 5 ) after the intensity equivalent of tem-
perature has been obtained through, say, equation (2a) or Figure 1. Intensity is important also as a prerequisite both to the development of the expressions for the evaluation of variable temperature schedules and to a very useful graphic presentation of a curing schedule, as shown below. CURIXG EFFECT-The first step in the determination of the curing effect of any given schedule is to divide the entire schedule into periods of uniform temperature gradient so that each becomes subject to the equations developed herein. Then a single period can in practice be evaluated in any one of several ways: (1) by direct use of one of the equations involving effect, E, as a variable, (2) by estimating the area under an intensity-time curve, or ( 3 ) by reading from a graph based upon one of the "effect" equations. (1) Computation fro?n Equation-Equation (6), ( 7 ) . or (9), or the expanded form of one of these, as shown in the summarizing table of equations, may be used for direct calculation of curing effect. Of these the expanded form of equation (6) is ordinarily the most useful as in it E is given in terms of quantities usually known without calculation-namely, initial temperature. time, and temperature gradient. Generally speaking. direct use of one of these equations is not the most convenient way of determining the curing effect; as a rule, either procedure (2) or (3) is more convenient. (2) Estimation of Area-Figure 2 illustrates how the intensity-time curve may be used to determine curing effect. The straight-line segment AB represents the temperaturetime relation of a cure period in which there is a uniform temperature gradient, here equal to 10" F. in 10 minutes (or m = 1). I n this case initial temperature, To. is 225" F.,
955
and time, t , after the attainment of To,is 65 minutes. The exponential curve CD is the corresponding intensity-time curve, and in view of the fundamental equation for curing effect, E =0 . d t
the area between C D and the time co6rtlinate, or CDEF, is proportional to effect. CD may be quickly drawn as a smooth curve through five or six points plotted from such almost selfevident values of intensity as I = for T = 225, 1 for T = 240, and 2 for T = 255, and so forth, or by plotting any other d u e s for intensity, as derivable at a glance from the intensity-temperature graph of Figure 1. The estimation of the area C D E F may be made in any of the well-known ways as, for example, by ( ( a ) use of the planimeter, ( b ) counting of squares, (c) weighing a piece of paper cut to the figure the area of which is to be e ~ t i m a t e d . ~The accuracy of any of these methods depends on the precision both with which the curve is drawn and with which its area is estimated, but the resultant accuracy greatly exceeds that of the basic empirical relation. For example, E for the case illustrated in Figure 2 when calculated from equation (6), equals 209; whereas when determined by counting squares under CD as actually drawn, for purposes of illustration rather than computation, we obtain E = 207. On two standard grades of graph paper deviations of 0.5 and 2.5 per cent, respectively, have been found in the weight of equal areas cut from different parts of the same sheet. The uniformity of graph paper is therefore seen to be somewhat variable and the paper-weighing method should be used only on paper that has been found to be uniform, and even then it is good practice to compare the weight of the cut-out for estimation with that of a rectangle of known area cut from the same piece of paper.
No attempt has been made in this paper to derive equation3 for E where the temperature gradient is non-uniform. There
are sereral reasons for this. Firstly, the great majority of variable temperature schedules, in strict conformity with the instructions for executing them, call for a series of uniform gradient periods and therefore fall within the scope of the relations here developed. Secondly, the integration to obk i n E for non-uniform gradients is more complicated and 3
Fol, I n d i a Rubber J . , 45, 679 (1913).
956
I X D V S T R I A L A N D ENGIA'EERING CHEMISTRY
leads to cumbersonie final equations, and is, moreover, unnecessary because the graphic method of estimating E of Figure 2 is applicable just as readily to variable as to constant temperature gradients. For a cure with a variable gradient, the procedure is to plot an intensity-time curve, based on the temperature-time relation (whether that be fixed by definition or empirically determined) and to estimate the area under this curve exactly as in the case of a uniform gradient.
Vol. 20, KO. 9
signed for the ready derivation of E , their construction, use, and limitations, will now be described. ( a ) Effect-time curves with gradient as variable parameter and with initial temperature fixed at 810 degrees. Figures 3 and 4, which differ only in their time scales, display families of curves, each of which plots the quantity El5.41 against t, the individual curves being subject to different values of m , and all curves being subject to the condition T O = 210" F. The values of m , ranging from 0 to 1 in Figure 3 and from 0 to 3 in Figure 4, and so chosen as to cover the gradients in most general use, are marked on the individual curves as fractions and in degrees per hour. \Then in the expanded form of equation (6) the substitution T,, = 210 is made, we get
By substituting in equation (10) successively the values of m , we get the equations which govern, and which have been used in computing, the values of E / 5 . 4 1 and of t for the individual curves. When it is desired to obtain the curing effect for an initial temperature of 210' F., the procedure is, on the curve for the given gradient, to read off for the time in question the value of El5.41 and to multiply this by .i.41. When, as usual, the initial temperature is higher than 210" F., the procedure is this: The value of E l 5 . 4 1 is read off for the specified gradient and for an initial temperature of 210' F., but for the time required to bring the temperature a t the gradient in question from 210' F. to the final temperature obtained by applying the specified gradient to the specified initial temperature. Also the value of E / 5 . 4 1 is read off for the specified gradient, for an initial temperature of 210' F., and for the time required to raise the temperature from 210" F. t o the specified initial temperature. The difference between the former va!ue of E / 5 . 4 1 and the latter multiplied by 5.41 yields theleff ect for the specified initial temperature.
The intensity-time curve, when drawn to nn equal-division scale, gives one the proper picture of the relative importance of the low and high temperatures of a schedule, something which the temperature-time graph does not do. This, of course, is because intensity is the quantity which measures the importance of a given temperature in promoting rulcanization. (3) Direct Reading from Graph. Considerable attention has been given to the development of graphs designed to show curing effect as a function of the other properties of a schedule, so that E might be read off directly without recourse in an individual case either to computation from an equation, as in (l),or to graphing the cure in terms of intensities with subsequent estimation of an area, as in ( 2 ) . It has not, however, seemed possible to devise any single graph which will enable effect to be read when the other properties which define the cure are given. The difficulty lies in the number of these other defining properties. The problem of graphicall~r presenting effect may be stated as that of drawing a locus for the equation connecting the dependent variable E with the three independent variables which are necessary to define a cure segment. For example, in the expanded form of equation (6), which is the most convenient one either for computation in a specific case or as the basis of a graph, the variables on which effect E depends and which define the cure are initial temperature, To, gradient, m, and time, f . The equation is therefore four-dimensional and incapable of graphic representation. This is true also of equations (7) and (9). While, therefore, the writers have been unable to accomplish the theoretical objective of displaying a graph which a t one reading and without any calculation would enable E to be read for any values of the other three variables, they have, however, designed several graphs which individually partially meet the objective, and which as a group accomplish in nine out of ten cases the practical purpose of enabling quick determination of E to be made. These several graphs de-
This working rule for deriving effect from Figure 3 or 4 in cases where the initial temperature is above that assumed in the construction of the graphs is, of course, based upon the fact that the effect is cumulative with time, that the total effect of a period is t h e sum of the separate effects for any parts into which the period may be divided. We may express the rule concisely by:
where
TO= given initial temperature T = the final temperature which follows from the values
of Tr, m,and t given As an example of deriving E from Figure 4 , let us take as a typical case the following numerical values : and t = 90 T o = 240, m = From equation ( 1 )
I-YDL'STRIAL A S D ENGISEERIil'G CHEMISTRY
September, 1928 T = 240
+ 90 - = 270 3
Time t o reach 2TO" from 210' F. = 180 minutes Time t o reach 240' from 210" F. = 90 minutes Then reading from Figure 4,
5 41 and
for the range 210' t o 270' F.-i.
e., for 180 minutes = 44.8
P.
~
__ for the range 210' t o 240' F.-i. e., for 90 minutes = 9.0 5 41 :. E for the specified conditions = (44.8-9.0) X 5.41 = 194 On account of its more open time scale, and therefore greater accuracy, Figure 4 is preferred t o Figure 3 for cases within its scope. There are two reasons for adopting E / 5 41 instead of E as the unit in the ordinate of these two sets of curves: ( a ) The ordinate of the graph form conveniently accommodates only 1000 units and, while 1000 is an unusually high value of E for cures used in practice, it is not nearly high enough, in cases where m is small and T Ohigh, for one of the hypothetical curesnamely, the one stretching from 210' F. t o the actual final temperature, which it is necessary, according t o its mode of usage, t o evaluate from the graph as a prerequisite to obtaining E for the given cure. Therefore, it is desirable t o make the unit space on the graph stand for a multiple of a unit of E . ( b ) The multiple chosen is 5.41, since it is convenient to use that numbrr (equation lo), and 5.41 increases the range of the graph in respect to E t o a fairly satisfactory degree. The disadvantages of Figures 3 and 4 as means of quick derivation of effect are: ( a ) the necessity of making two readings with some prior (though simple) calculations; ( b ) the effect can be read only for those gradients shown on the graphs; (c) notwithstanding the use (in both figures) of E/5.41 as unit for the ordinate and an unusually great time range (in one of the figures), cures with quite low gradients and high initial temperatures will be found outside the range of either figure. Within their ranges, however, Figures 3 and 4 are usable for all gradients marked on them and these are the more common ones. Table I-Summary PROCEDURE
DESCRIPTION OB GRAPH
......
(1)
T - t a n d I - I curves Typical case only
( b ) Effect-initial temperature curties with gradient as variable parameter and with time $xed at 60,15, and 5 minutes, respectively, f o r each of three families of curves. I n Figure 5, E is plotted against T O ,each line being subject t o the value of m with which it is marked and t o the value of t with which the entire family of curves t o which it belongs is marked. There are three families in the one graph subject, respectively, t o the following values of t-60, 15, and 5 minutes. The values of the parameter m range from 0 t o 3 except in the fami!y where t = 60 minutes, wherein m ranges from 0 t o 2. In the family subject t o t = 5 it has been possible, on account of the proximity of lines to each other, t o use only a limited number of values of m; for t = 15 and for t = 60 more numerous values of m are capable of display. The curves in each family of Figure 5 have been computed by substituting in the expanded form of equation (6) a value for t . When this value is t = 15, we get from equation (6) To - 240
21.64 (2"'--1) 2~ (12) m The equation for an individual line is then obtained by substituting a value for m in equation (12). As the resulting equation is exponential in E and Ti, the plot is a straight line on the semilogarithmic graph paper. The other two families are based on equations analogous to (12), obtained by substituting 60 and 5 , respectively, for t in equation ( 6 ) . Figure 5 yields a t once a reading for the effect of any cure within its range and subject to a gradient shown and to a time of 5, 15, or 60 minutes. When the time is otherwise than one of these three periods but is a multiple of 5 minutes, the procedure is to break the period up into sections such that each involves one of these three displayed times. As an example we may take the numerical values used in illustrating procedure ( a ) , Tu= 240, m = t = 90 E for 60 minutes, going from 240" to 260" F. = 100 E for 15 minutes, going from 260" t o 265' F. = 41.8 E for 15 minutes, going from 265' t o 270" F. = 51.4
E =
___
.'.E for 80 minutes going from 240" to 280" F. = 193
of Procedures for Determining Curing Effect
PROCESS I N BRIEF
ADVAXTAGES
Most accurate method, and one Usually most laborious method on which all others deDend
Estimate E from area under a n I - t curve, as determined i n one of following mays:
(1) An intensity graph is obtained which is per se useful, a s affording a truer picture of curing tendencies t h a n a temperature graph ( 2 ) Always applicable, even t o conditions outside range of Figures 3, 4, 5 , 6, and 7 and t o cases of variable gradient, not covered b y equations Probably quickest way t o estimate area
B y counting squares B y weighing paper cut-out
Read E directly f r o m one of graphs involving E a s variable, as given below:
E
-t
curves, with m as variable parameter and To constant a t 210
- To curves, with m as variable
parameter and with t fixed 15, a t three values-60, and 5
E - m curves, with To as variable parameter and with I fixed a t three v a l u e s 4 0 , 16, and 5
DISADVASTAOES
Compute E from a n equatione. g., equation ( 6 )
B y planimeter
E
957
F o r given gradient read E/5.41 for time necessary t o raise T from 210 t o (1) given final temperature, ( 2 ) given initial temperature. Subtract (2) f r o m (1) a n d multiply b y 5.41
Conversion of temperatures into intensities, graphing of latter, and estimation of area under curve, usuallyrequire moretime than reading E from graph a s i n method (3)
I Applicable only t o graph paper of ascertained uniformity of weight
Quickest way t o obtain E for all cases within limitations of graphs, a s involving no graphing a n d none or a minim u m of calculation Handles any time period within range of Figures 3 a n d 4, and without necessity of breaking it u p into arbitrary p a r t s with reading of E for separate parts
(1) Applicable t o any initial
Divide cure into periods of 60, 15, and 5 minutes, and for each read E for given gradient, a n d for value of 1 and To pertaining t o period. S u m of these several values of E is E f o r given period
temperature within range of graph (2) More accurate t h a n ( a ) , for reason stated under ( a ) (3) Reads directly in E ; n o multiplication necessary
Proceed exactly as in (bj above
(1) Appgcable t o any gradient
and initial temperature within range of t h e graphs. Equal spacing of curves makes Interpolation for unmarked values of To easy ( 2 ) More accurate t h a n ( a ) for reason stated under ( a ) (3) Reads directly in E ; no multiplication necessary
Limited t o cases within range of one or other graph
~
(1) ,Limited t o individual gradients and time range used i l l Figures 3 and 4 ( 2 ) Necessary usually t o make two readings (3) Necessary t o multiply reading b y 5 . 4 1 (4) Less accurate t h a n ( b ) or ( c ) , because of necessarily more condensed E scale (1) Limited t o individual gradients shown in figure ( 2 ) Limited t o periods which are multiples of 5 minutes (3) Necessary usually t o subdivide period a n d make separ a t e readings for t h e several Darts
I-VD USTRIAL d S D EAL’GINEERI,VGCHEXISTRY
958
Compared with Figures 3 and 4, the advantages of Figure 5 are: ( a ) it has greater accuracy due to its more open E scale; (b) cases as a rule can be determined by it somewhat more quickly than by Figure 3 or 4. The disadvantages of Figure 5 are: ( a ) the limited number of gradients displayed, particularly for the 5-minute cure; (b) cures t o be handled must have time periods which are multiples of 5 minutes. Figure 5 is preferred to 3 or 4 for cases within its range. (c) E f e c t - g r a d i e n t curves with initial temperatures as variable parameter and with timefixed at 60, 15, and 5 minutes, respectively, for each of three families of curves. In Figure 6 there is plotted E against m, TO being shown as a variable parameter, and t being constant a t 60 minutes. Figure 7 employs the same variables and variable parameter, but in this two families of curves are shown characterized, r e s p e c tively, by t = 15 and t = 5. These figures have been graphed from the same data employed in graphing Figure 5namely, data derived from equation (12). The essential difference between Figures 6 and 7 and Figure 5 lies in what have been chosen as ingependent variable and as variable parameter. These figures are used very similarly t o Figure 5, by dividing the cure into parts of 60, 15, and 5 minutes’ duration and finding E for the whole as the sum of the values of E for the parts. Compared with Figure 5 , Figures 6 and 7 have the advantage of covering all gradients within their range, but the disadvantage of having initial temperature displayed a t only fixed intervals as a parameter. This disadvantage, however, will not be found so objectionable as the parametric treatment of gradient in Figure 5 or Figures 3 and 4. It will be found almost as easy in Figures 6 and 7 to estimate the position of a curve corresponding with an initial temperature not shown on the graph as t o estimate intermediate values on the gradient or effect scales. Generally speaking, procedure (c) is more convenient than procedure ( a ) or ( b ) and is preferred when applicable. Procedure (c), like ( b ) , is limited to cases where the duration is a multiple of 5 minutes. SUllMARY O F
PROCEDURES
FOR
Vol. 20, KO. 9
and in the attainment of a curing effect, up to the point R a t the end of the “drying out” period, of only 34 out of a total of 391 for the whole schedule. Contrasted with this in an unmistakable manner by the mode of display used is the quick attainment of a curing condition in the “surf” cure. The temperature curves for these two schedules fail to convey, except by inference, the important fact that a t its highest temperature the “heavy” heat is promoting vulcanization twice as actively as the “surf” a t its peak. This fact is, however, expressed directly by the intensity curves through their relative heights. It is for reasons of which this is but a particular case that the miters believe the plotting of intensities greatly to promote the clear conception of vulcanizer schedules where variable temperatures are employed. The curing effects shown in the upper left corner of Figure 8, and also on Figures 9 to 11, were obtained by direct reading from one or other of the “effect” graphs-Figures 3 to 7. Extreme accuracy is neither to be expected nor, in view of the only approximate character of the basic relation, necessary. An agreement within about 1 per cent, as among evaluations read from different “effect” graphs or as between such an evaluation and the “correct” value got by calculation, may be expected. Table I1 brings out this point. It details the values of E obtained by various procedures for the several
DETERXINISGC U R I X G
EFFECT-In the belief that a table of the several procedures for determining curing effect, summarizing the advantages and limitations of each, will aid in the choice of the best method for a given case, Table I has been drawn up. In general the writers’ preference is to display a cure through both temperature-time and intensity-time graphs similar to Figure 2, but to evaluate it by reading the curing effects ( E ) of its several uniform gradient segments directly from one of the “effect” graphs. Illustrations f r o m P l a n t Practice
Figures 8 to 11 show some typical curing schedules illustrating a variety both of product and of type of cure, and graphed to display intensities as well as temperatures. The intensity-time curves are the lowest ones, the areas subtended by which are shaded and (as between the several schedules in each figure) are proportional to the curing effects. The curing effects have been tabulated on each graph for the cures displayed thereon. Figure 8 shows three footwear box cures, of quite diverse curing effects, the “heavy” cure being about 66 per cent more severe than the lightest or “surf” (bathing shoe). The restrained curing activity of the “heavy” heat during its preliminary “warming up” and “drying out” periods, ABFK, is well reflected in the corresponding low-lying intensity curve
segments of the “heavy” cure in Figure 8. Agreements of the same order were obtained in evaluating the effects for the other schedules illustrated. In Figure 9 two dry-heat cures, with air pressure, for footwear are shown. Although there is a considerable divergence between the two schedules, they are in general of the same order of curing effect as the box heats of Figure 8. That such is the case, notwithstanding their much shorter durations, is of course due to the higher intensities employed in the pressure cures and also to the much more abrupt “rise.” Schedules for dry-heat cures on proofed goods of single and double texture are given in Figure 10. That single textures are given a dryer or more complete cure than double textures is a matter of common knowledge, but that the single cure has three times the severity of the double is hardly obvious even from an inspection of the temperature schedules. The curing effects bring out this more exact relation in the severities, however, and the intensity graphs with their subtended areas create an impression of the same outstanding difference in the two cures.
September, 1928
111'DCSTRIAL A S D E-\-GIiVEERING CHEMIXTRY
959
Kevertheless it is useful here, as in the other cases, to plot an intensity-time graph. It will be noted from Figure 11 that, although the schedules for the two tires are quite different in their total times, their curing effects are only moderately different. This, of course, is consequent upon that segment responsible for most of the curing, the one a t 298' F., being of equal duration for both cases (120 minutes), the diversity of time being in the early, low-intensity portions, comparatively unimportant from the standpoint of vulcanization (but of course essential to heat penetration). Table 11-Values
of E for Various Parts of Heavy Footaear Box Cure a s Derived by Several Procedures
1 PERIOD
AB
310
--
BF
To
t
m
160
60
l/3
180
180
E
OBTAINED B Y PROCEDURE
(3) ( a ) (3) ( b ) (1) Read from Read from Calcd. Figures Figure from Fig3 and4 5 ures6and7
I
..
..
..
2.1
i:7 12.0
4.7 7.7 12.2
3.75 3.75
__
FK
210
30
0
KL
210
60
1/6
-24.6
'/a
1
3.75 3.75 __
7.5
7.6
7.5
7.5
..
19.2
19.2
19.4 ~
35 3 69 5 138 5
Lhl
220
180
244 5
243 3 46 8 46 8
Figure 11 shows cures for 3l/* and &inch solid tires. These schedules, although "stepped," do not involve variable temperatures in the sense of a variation within a given step or segment of the cure. They can, therefore, contrary to the cases illustrated in Figures 8, 9, and 10, be evaluated without recourse to one of the equations developed herein for variabletemperature cures or to any graphic method depending upon these equations, simply by taking the curing effect of each segment as the product of its time and intensity (equation 5).
47 0 47 0
Swedish Company to Manufacture Solid Carbon Dioxide--A Swedish company has recently announced that it will start making ice out of some of the liquid carbon dioxide a t present produced in its plant. After watching the use of DryIce in the United States, the Swedish company believes that there will be a market for the same product in Sweden once the consumers become convinced of the advantages of the solidified carbon dioxide over the natural ice. The volume of production will be small t o begin with, but it is hoped that the demand will gradiially increase.
